Viviani, Vincenzo, De maximis et minimis, geometrica divinatio : in qvintvm Conicorvm Apollonii Pergaei

Table of contents

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[141.] THEOR. XXIX. PROP. LIIX.
Page: 126 (102)
[142.] ALITER.
Page: 126 (102)
[143.] THEOR. XXX. PROP. LIX.
Page: 127 (103)
[144.] THEOR. XXXI. PROP. LX.
Page: 127 (103)
[145.] THEOR. XXXII. PROP. LXI.
Page: 128 (104)
[146.] THEOR. XXXIII. PROP. LXII.
Page: 129 (105)
[147.] SCHOLIVM.
Page: 130 (106)
[148.] THEOR. XXXIV. PROP. LXIII.
Page: 131 (107)
[149.] THEOR. XXXV. PROP. LXIV.
Page: 131 (107)
[150.] PROBL. XXIV. PROP. LXV.
Page: 132 (108)
[151.] LEMMA VII. PROP. LXVI.
Page: 133 (109)
[152.] SCHOLIVM.
Page: 133 (109)
[153.] PROBL. XXV. PROP. LXVII.
Page: 134 (110)
[154.] MONITVM.
Page: 134 (110)
[155.] PROBL. XXVI. PROP. LXVIII.
Page: 135 (111)
[156.] PROBL. XXVII. PROP. LXIX.
Page: 137 (113)
[157.] PROBL. XXVIII. PROP. LXX.
Page: 138 (114)
[158.] LEMMA VIII. PROP. LXXI.
Page: 139 (115)
[159.] LEMMA IX. PROP. LXXII.
Page: 140 (116)
[160.] PROBL. XXIX. PROP. LXXIII.
Page: 141 (117)
[161.] LEMMA X. PROP. LXXIV.
Page: 141 (117)
[162.] PROBL. XXX. PROP. LXXV.
Page: 142 (118)
[163.] COROLL. I.
Page: 143 (119)
[164.] COROLL. II.
Page: 143 (119)
[165.] MONITVM.
Page: 143 (119)
[166.] THEOR. XXXVI. PROP. LXXVI.
Page: 144 (120)
[167.] SCHOLIVM.
Page: 145 (121)
[168.] THEOR. XXXVII. PROP. LXXVII.
Page: 146 (122)
[169.] PROBL. XXXI. PROP. LXXVIII.
Page: 147 (123)
[170.] MONITVM.
Page: 148 (124)
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          <head xml:id="echoid-head177" xml:space="preserve">LEMMA XII. PROP. LXXX.</head>
          <p>
            <s xml:id="echoid-s4221" xml:space="preserve">Si fuerit rectangulum ABC, ęquale rectangulo DEF, ſitque AC
              <lb/>
            maior DF, erit BC minor EF.</s>
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            <image file="0149-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/QN4GHYBF/figures/0149-01"/>
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            <s xml:id="echoid-s4223" xml:space="preserve">SI enim dicatur BC æqualem, vel maiorem
              <lb/>
            eſſe EF, cum ſit data AC maior DF, eſſet
              <lb/>
            omnino AB maior DE, & </s>
            <s xml:id="echoid-s4224" xml:space="preserve">BC dicitur æqualis,
              <lb/>
            vel maior EF, ergo rectangulum ABC eſſet om-
              <lb/>
            nino maius rectangulo DEF, ſed æquale poſi-
              <lb/>
            tum fuit. </s>
            <s xml:id="echoid-s4225" xml:space="preserve">Ergo patet propoſitum.</s>
            <s xml:id="echoid-s4226" xml:space="preserve"/>
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        <div xml:id="echoid-div409" type="section" level="1" n="173">
          <head xml:id="echoid-head178" xml:space="preserve">THEOR. XXXVIII. PROP. LXXXI.</head>
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            <s xml:id="echoid-s4227" xml:space="preserve">Si recta linea ad alterũ terminũ cuiuſdam applicatæ coni-ſectio-
              <lb/>
            nem, vel circulũ cõtingat, ipſa omnino ſecabit ſibi adſcriptã eiuſdẽ
              <lb/>
            nominis ſectionẽ circa eandẽ applicatam, & </s>
            <s xml:id="echoid-s4228" xml:space="preserve">cum æquali tranſuerſa
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            diametro, ſi ſectiones fuerint Hyperbolæ, vel Ellipſes, aut circuli.</s>
            <s xml:id="echoid-s4229" xml:space="preserve"/>
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            <s xml:id="echoid-s4230" xml:space="preserve">ESto quæcunque coni-ſectio, vel circulus ABC, cuius diameter BD, yo
              <unsure/>
              <lb/>
            vna applicatarum ſit AC. </s>
            <s xml:id="echoid-s4231" xml:space="preserve">& </s>
            <s xml:id="echoid-s4232" xml:space="preserve">ad ipſius terminum A, ſit recta contingens
              <lb/>
            EAF, quæ diametro occurret in F; </s>
            <s xml:id="echoid-s4233" xml:space="preserve">& </s>
            <s xml:id="echoid-s4234" xml:space="preserve">ſumpto in diametri ſegmento
              <note symbol="a" position="right" xlink:label="note-0149-01" xlink:href="note-0149-01a" xml:space="preserve">24. 25.
                <lb/>
              pr. conic.</note>
            quolibet puncto G, cum diametro GD, & </s>
            <s xml:id="echoid-s4235" xml:space="preserve">applicata AC in qualibet figura,
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            ſed etiam, pro Hyperbola in ſecunda, & </s>
            <s xml:id="echoid-s4236" xml:space="preserve">pro Ellipſi, vel circulo, in tertia,
              <lb/>
            cum dato tranſuerſo latere GM, quod æquale ſit tranſuerſo BL datæ ſectio-
              <lb/>
            nis, deſcribatur eiuſdem nomin@s ſectio AGC: </s>
            <s xml:id="echoid-s4237" xml:space="preserve">dico hanc omnino
              <note symbol="b" position="right" xlink:label="note-0149-02" xlink:href="note-0149-02a" xml:space="preserve">57. h.</note>
            contingente EAF.</s>
            <s xml:id="echoid-s4238" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s4239" xml:space="preserve">Ducatur enim per A recta IAH, quæ ſectionem continge
              <unsure/>
            t AGC, cum
              <lb/>
            eius diametro conueniat in H.</s>
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            <s xml:id="echoid-s4241" xml:space="preserve">Iam in prima figura exhiben@ Parabolas, cum AF contingat </s>
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